Quantal puffs of intracellular Ca2+ evoked by inositol trisphosphate in Xenopus oocytes

Inositol-1,4,5-trisphosphate receptor-mediated Ca2+ waves in pyramidal neuron dendrites propagate through hot spots and cold spots

We studied inositol-1,4,5-trisphosphate (IP(3)) receptor-dependent intracellular Ca(2+) waves in CA1 hippocampal and layer V medial prefrontal cortical pyramidal neurons using whole-cell patch-clamp recordings and Ca(2+) fluorescence imaging. We observed that Ca(2+) waves propagate in a saltatory manner through dendritic regions where increases in the intracellular concentration of Ca(2+) ([Ca(2+)](i)) were large and fast ('hot spots') separated by regions where increases in [Ca(2+)](i) were comparatively small and slow ('cold spots'). We also observed that Ca(2+) waves typically initiate in hot spots and terminate in cold spots, and that most hot spots, but few cold spots, are located at dendritic branch points. Using immunohistochemistry, we found that IP(3) receptors (IP(3)Rs) are distributed in clusters along pyramidal neuron dendrites and that the distribution of inter-cluster distances is nearly identical to the distribution of inter-hot spot distances. These findings support the hypothesis that the dendritic locations of Ca(2+) wave hot spots in general, and branch points in particular, are specially equipped for regenerative IP(3)R-dependent internal Ca(2+) release. Functionally, the observation that IP(3)R-dependent [Ca(2+)](i) rises are greater at branch points raises the possibility that this novel Ca(2+) signal may be important for the regulation of Ca(2+)-dependent processes in these locations. Futhermore, the observation that Ca(2+) waves tend to fail between hot spots raises the possibility that influences on Ca(2+) wave propagation may determine the degree of functional association between distinct Ca(2+)-sensitive dendritic domains.

Simplified model of cytosolic Ca2+ dynamics in the presence of one or several clusters of Ca2+ -release channels

Calcium release from intracellular stores plays a key role in the regulation of a variety of cellular activities. In various cell types this release occurs through inositol-triphosphate (IP3) receptors which are Ca2+ channels whose open probability is modulated by the cytosolic Ca2+ concentration itself. Thus, the combination of Ca2+ release and Ca2+ diffusion evokes a variety of Ca2+ signals depending on the number and relative location of the channels that participate of them. In fact, a hierarchy of Ca2+ signals has been observed in Xenopus laevis oocytes, ranging from very localized events (puffs and blips) to waves that propagate throughout the cell. In this cell type channels are organized in clusters. The behavior of individual channels within a cluster cannot be resolved with current optical techniques. Therefore, a combination of experiments and mathematical modeling is unavoidable to understand these signals. However, the numerical simulation of a detailed mathematical model of the problem is very hard given the large range of spatial and temporal scales that must be covered. In this paper we present an alternative model in which the cluster region is modeled using a relatively fine grid but where several approximations are made to compute the cytosolic Ca2+ concentration ([Ca;{2+}]) distribution. The inner-cluster [Ca;{2+}] distribution is used to determine the openings and closings of the channels of the cluster. The spatiotemporal [Ca;{2+}] distribution outside the cluster is determined using a coarser grid in which each (active) cluster is represented by a point source whose current is proportional to the number of open channels determined before. A full reaction-diffusion system is solved on this coarser grid.

Localization of puff sites adjacent to the plasma membrane: functional and spatial characterization of Ca2+ signaling in SH-SY5Y cells utilizing membrane-permeant caged IP3

The Xenopus oocyte has been a favored model system in which to study spatio-temporal mechanisms of intracellular Ca2+ dynamics, in large part because this giant cell facilitates intracellular injections of Ca2+ indicator dyes, buffers and caged compounds. However, the recent commercial availability of membrane-permeant ester forms of caged IP3 (ci-IP3) and EGTA, now allows for facile loading of these compounds into smaller mammalian cells, permitting control of [IP3]i and cytosolic Ca2+ buffering. Here, we establish the human neuroblastoma SH-SY5Y cell line as an advantageous experimental system for imaging Ca2+ signaling, and characterize IP3-mediated Ca2+ signaling mechanisms in these cells. Flash photo-release of increasing amounts of i-IP3 evokes Ca2+ puffs that transition to waves, but intracellular loading of EGTA decouples release sites, allowing discrete puffs to be studied over a wide range of [IP3]. Puff activity persists for minutes following a single photo-release, pointing to a slow rate of i-IP3 turnover in these cells and suggesting that repetitive Ca2+ spikes with periods of 20-30s are not driven by oscillations in [IP3]. Puff amplitudes are independent of [IP3], whereas their frequencies increase with increasing photo-release. Puff sites in SH-SY5Y cells are not preferentially localized near the nucleus, but instead are concentrated close to the plasma membrane where they can be visualized by total internal reflection microscopy, offering the potential for unprecedented spatio-temporal resolution of Ca2+ puff kinetics.

Markov chain models of coupled calcium channels: Kronecker representations and iterative solution methods

Mathematical models of calcium release sites derived from Markov chain models of intracellular calcium channels exhibit collective gating reminiscent of the experimentally observed phenomenon of stochastic calcium excitability (i.e., calcium puffs and sparks). Calcium release site models are stochastic automata networks that involve many functional transitions, that is, the transition probabilities of each channel depend on the local calcium concentration and thus the state of the other channels. We present a Kronecker-structured representation for calcium release site models and perform benchmark stationary distribution calculations using both exact and approximate iterative numerical solution techniques that leverage this structure. When it is possible to obtain an exact solution, response measures such as the number of channels in a particular state converge more quickly using the iterative numerical methods than occupation measures calculated via Monte Carlo simulation. In particular, multi-level methods provide excellent convergence with modest additional memory requirements for the Kronecker representation of calcium release site models. When an exact solution is not feasible, iterative approximate methods based on the power method may be used, with performance similar to Monte Carlo estimates. This suggests approximate methods with multi-level iterative engines as a promising avenue of future research for large-scale calcium release site models.

Functional architecture of inositol 1,4,5-trisphosphate signaling in restricted spaces of myoendothelial projections

Calcium (Ca(2+)) release through inositol 1,4,5-trisphosphate receptors (IP(3)Rs) regulates the function of virtually every mammalian cell. Unlike ryanodine receptors, which generate local Ca(2+) events ("sparks") that transmit signals to the juxtaposed cell membrane, a similar functional architecture has not been reported for IP(3)Rs. Here, we have identified spatially fixed, local Ca(2+) release events ("pulsars") in vascular endothelial membrane domains that project through the internal elastic lamina to adjacent smooth muscle membranes. Ca(2+) pulsars are mediated by IP(3)Rs in the endothelial endoplasmic reticulum of these membrane projections. Elevation of IP(3) by the endothelium-dependent vasodilator, acetylcholine, increased the frequency of Ca(2+) pulsars, whereas blunting IP(3) production, blocking IP(3)Rs, or depleting endoplasmic reticulum Ca(2+) inhibited these events. The elementary properties of Ca(2+) pulsars were distinct from ryanodine-receptor-mediated Ca(2+) sparks in smooth muscle and from IP(3)-mediated Ca(2+) puffs in Xenopus oocytes. The intermediate conductance, Ca(2+)-sensitive potassium (K(Ca)3.1) channel also colocalized to the endothelial projections, and blockage of this channel caused an 8-mV depolarization. Inhibition of Ca(2+) pulsars also depolarized to a similar extent, and blocking K(Ca)3.1 channels was without effect in the absence of pulsars. Our results support a mechanism of IP(3) signaling in which Ca(2+) release is spatially restricted to transmit intercellular signals.

Calcium signalling in smooth muscle

Calcium signalling in smooth muscles is complex, but our understanding of it has increased markedly in recent years. Thus, progress has been made in relating global Ca2+ signals to changes in force in smooth muscles and understanding the biochemical and molecular mechanisms involved in Ca2+ sensitization, i.e. altering the relation between Ca2+ and force. Attention is now focussed more on the role of the internal Ca2+ store, the sarcoplasmic reticulum (SR), global Ca2+ signals and control of excitability. Modern imaging techniques have shown the elaborate SR network in smooth muscles, along with the expression of IP3 and ryanodine receptors. The role and cross-talk between these two Ca(2+) release mechanisms, as well as possible compartmentalization of the SR Ca2+ store are discussed. The close proximity between SR and surface membrane has long been known but the details of this special region to Ca2+ signalling and the role of local sub-membrane Ca2+ concentrations and membrane microdomains are only now emerging. The activation of K+ and Cl- channels by local Ca2+ signals, can have profound effects on excitability and hence contraction. We examine the evidence for both Ca2+ sparks and puffs in controlling ion channel activity, as well as a fundamental role for Ca2+ sparks in governing the period of inexcitability in smooth muscle, i.e. the refractory period. Finally, the relation between different Ca2+ signals, e.g. sparks, waves and transients, to smooth muscle activity in health and disease is becoming clearer and will be discussed.

Modulation of calcium signals by fluorescent dyes in the presence of tubular endoplasmic reticulum: a modelling approach

The complex network of Ca(2+) signals uses local events as building blocks for generating global calcium signals with different shapes. However, the nature of the large time- and space-scales of local calcium signals observed in Xenopus oocytes has remained unclear. By numeric simulations that include optical blurring of the image and the geometrical restrictions imposed by tubules of the endoplasmic reticulum or other cell structures, we investigate how the fluorescent dye affect the observed features of calcium events, such as rate of signal decay, spatial size, fluorescence amplitude, or the apparent diffusion like from a point source in a spherically symmetric space. We add more evidence that, irrespective of the dye properties, local calcium signals produced in the presence of tubular cellular structures are consistently wider than expected in a homogeneous environment. Moreover, the spatial dimension and the decay time of the event increase with the quantity of liberated Ca(2+). Our results also indicate that a fast binding Ca(2+) indicator that does not bind to cytosolic proteins yields fast signals when the event is observed in the front of the release site, and slow signals when the event is viewed from the opposite side of the tubule. We propose several ways to test our model by various experimental procedures.

Calcium-dependent inactivation and the dynamics of calcium puffs and sparks

Localized intracellular Ca(2+) elevations known as puffs and sparks arise from the cooperative activity of inositol 1,4,5-trisphosphate receptor Ca(2+) channels (IP(3)Rs) and ryanodine receptor Ca(2+) channels (RyRs) clustered at Ca(2+) release sites on the surface of the endoplasmic reticulum or sarcoplasmic reticulum. When Markov chain models of these intracellular Ca(2+)-regulated Ca(2+) channels are coupled via a mathematical representation of a Ca(2+) microdomain, simulated Ca(2+) release sites may exhibit the phenomenon of "stochastic Ca(2+) excitability" reminiscent of Ca(2+) puffs and sparks where channels open and close in a concerted fashion. To clarify the role of Ca(2+) inactivation of IP(3)Rs and RyRs in the dynamics of puffs and sparks, we formulate and analyze Markov chain models of Ca(2+) release sites composed of 10-40 three-state intracellular Ca(2+) channels that are inactivated as well as activated by Ca(2+). We study how the statistics of simulated puffs and sparks depend on the kinetics and dissociation constant of Ca(2+) inactivation and find that puffs and sparks are often less sensitive to variations in the number of channels at release sites and strength of coupling via local [Ca(2+)] when the average fraction of inactivated channels is significant. Interestingly, we observe that the single channel kinetics of Ca(2+) inactivation influences the thermodynamic entropy production rate of Markov chain models of puffs and sparks. While excessively fast Ca(2+) inactivation can preclude puffs and sparks, moderately fast Ca(2+) inactivation often leads to time-irreversible puffs and sparks whose termination is facilitated by the recruitment of inactivated channels throughout the duration of the puff/spark event. On the other hand, Ca(2+) inactivation may be an important negative feedback mechanism even when its time constant is much greater than the duration of puffs and sparks. In fact, slow Ca(2+) inactivation can lead to release sites with a substantial fraction of inactivated channels that exhibit puffs and sparks that are nearly time-reversible and terminate without additional recruitment of inactivated channels.

How does intracellular Ca2+ oscillate: by chance or by the clock?

Ca2+ oscillations have been considered to obey deterministic dynamics for almost two decades. We show for four cell types that Ca2+ oscillations are instead a sequence of random spikes. The standard deviation of the interspike intervals (ISIs) of individual spike trains is similar to the average ISI; it increases approximately linearly with the average ISI; and consecutive ISIs are uncorrelated. Decreasing the effective diffusion coefficient of free Ca2+ using Ca2+ buffers increases the average ISI and the standard deviation in agreement with the idea that individual spikes are caused by random wave nucleation. Array-enhanced coherence resonance leads to regular Ca2+ oscillations with small standard deviation of ISIs.

Modeling Ca2+ signaling differentiation during oocyte maturation

Ca2+ is a fundamental intracellular signal that mediates a variety of disparate physiological functions often in the same cell. Ca2+ signals span a wide range of spatial and temporal scales, which endow them with the specificity required to induce defined cellular functions. Furthermore, Ca2+ signaling is highly plastic as it is modulated dynamically during normal physiological development and under pathological conditions. However, the molecular mechanisms underlying Ca2+ signaling differentiation during cellular development remain poorly understood. Oocyte maturation in preparation for fertilization provides an exceptionally well-suited model to elucidate Ca2+ signaling regulation during cellular development. This is because a Ca2+ signal with specialized spatial and temporal dynamics is universally essential for egg activation at fertilization. Here we use mathematical modeling to define the critical determinants of Ca2+ signaling differentiation during oocyte maturation. We show that increasing IP3 receptor (IP3R) affinity replicates both elementary and global Ca2+ dynamics observed experimentally following oocyte maturation. Furthermore, our model reveals that because of the Ca2+ dependency of both SERCA and the IP3R, increased IP3R affinity shifts the system's equilibrium to a new steady state of high cytosolic Ca2+, which is essential for fertilization. Therefore our model provides unique insights into how relatively small alterations of the basic molecular mechanisms of Ca2+ signaling components can lead to dramatic alterations in the spatio-temporal properties of Ca2+ dynamics.

Discrete influx events refill depleted Ca2+ stores in a chick retinal neuron

The depletion of ER Ca2+ stores, following the release of Ca2+ during intracellular signalling, triggers the Ca2+ entry across the plasma membrane known as store-operated calcium entry (SOCE). We show here that brief, local [Ca2+]i increases (motes) in the thin dendrites of cultured retinal amacrine cells derived from chick embryos represent the Ca2+ entry events of SOCE and are initiated by sphingosine-1-phosphate (S1P), a sphingolipid with multiple cellular signalling roles. Externally applied S1P elicits motes but not through a G protein-coupled membrane receptor. The endogenous precursor to S1P, sphingosine, also elicits motes but its action is suppressed by dimethylsphingosine (DMS), an inhibitor of sphingosine phosphorylation. DMS also suppresses motes induced by store depletion and retards the refilling of depleted stores. These effects are reversed by exogenously applied S1P. In these neurons formation of S1P is a step in the SOCE pathway that promotes Ca2+ entry in the form of motes.

Mode switching is the major mechanism of ligand regulation of InsP3 receptor calcium release channels

The inositol 1,4,5-trisphosphate (InsP₃) receptor (InsP₃R) plays a critical role in generation of complex Ca²⁺ signals in many cell types. In patch clamp recordings of isolated nuclei from insect Sf9 cells, InsP₃R channels were consistently detected with regulation by cytoplasmic InsP₃ and free Ca²⁺ concentrations ([Ca²⁺]_i) very similar to that observed for vertebrate InsP₃R. Long channel activity durations of the Sf9-InsP₃R have now enabled identification of a novel aspect of InsP₃R gating: modal gating. Using a novel algorithm to analyze channel modal gating kinetics, InsP₃R gating can be separated into three distinct modes: a low activity mode, a fast kinetic mode, and a burst mode with channel open probability (P_o) within each mode of 0.007 ± 0.002, 0.24 ± 0.03, and 0.85 ± 0.02, respectively. Channels reside in each mode for long periods (tens of opening and closing events), and transitions between modes can be discerned with high resolution (within two channel opening and closing events). Remarkably, regulation of channel gating by [Ca²⁺]_i and [InsP₃] does not substantially alter channel P_o within a mode. Instead, [Ca²⁺]_i and [InsP₃] affect overall channel P_o primarily by changing the relative probability of the channel being in each mode, especially the high and low P_o modes. This novel observation therefore reveals modal switching as the major mechanism of physiological regulation of InsP₃R channel activity, with implications for the kinetics of Ca²⁺ release events in cells.

Calcium sparks activate calcium-dependent Cl− current in rat corpus cavernosum smooth muscle cells

Spontaneous transient currents, due to activation of Ca2+-dependent K+ and Cl− channels, occur in corpus cavernosum smooth muscle cells (CCSMC) of the penis. The Ca2+ events responsible for triggering Ca2+-dependent Cl− channels have never been identified in vascular muscle. We used high-speed fluorescence imaging combined with patch-clamp electrophysiology to provide the first characterization of Ca2+ events underlying these currents. Freshly isolated rat CCSMC loaded with fluo-4 exhibited localized, spontaneous elevations of intracellular Ca2+ (Ca2+ sparks) in 57% of cells. There was an average of 6.4 ± 0.5 release sites/cell with a frequency of 0.9 ± 1 Hz/cell and peak amplitude ΔF/Fo of 67 ± 10%. We addressed the controversy of whether these events are mediated by ryanodine or inositol 1,4,5 trisphosphate (IP3) receptors. Caffeine caused either a global Ca2+ rise at high concentrations or an increase in spark frequency at lower concentrations, whereas ryanodine dramatically reduced the amplitude and frequency of sparks. 2-Aminoethoxydiphenyl borate, an inhibitor of IP3 receptors, had no effect on spark frequency. Combined imaging and electrophysiological recording revealed strong coupling between Ca2+ sparks and biphasic transient currents, a relationship never before shown in vascular muscle. Moreover, spark frequency increased on depolarization, an effect abolished with the blockade of Ca2+ channels, consistent with Ca2+ influx regulating Ca2+ release from stores. We establish for the first time that Ca2+ sparks occur in CCSMC and arise from Ca2+ release through ryanodine receptors. Moreover, the voltage dependence of spark frequency demonstrated here provides novel functional evidence for voltage-dependent Ca2+ influx in CCSMC.

A bidomain threshold model of propagating calcium waves

We present a bidomain fire-diffuse-fire model that facilitates mathematical analysis of propagating waves of elevated intracellular calcium (Ca(2+)) in living cells. Modeling Ca(2+) release as a threshold process allows the explicit construction of traveling wave solutions to probe the dependence of Ca(2+) wave speed on physiologically important parameters such as the threshold for Ca(2+) release from the endoplasmic reticulum (ER) to the cytosol, the rate of Ca(2+) resequestration from the cytosol to the ER, and the total [Ca(2+)] (cytosolic plus ER). Interestingly, linear stability analysis of the bidomain fire-diffuse-fire model predicts the onset of dynamic wave instabilities leading to the emergence of Ca(2+) waves that propagate in a back-and-forth manner. Numerical simulations are used to confirm the presence of these so-called 'tango waves' and the dependence of Ca(2+) wave speed on the total [Ca(2+)].

Multi-dimensional resolution of elementary Ca2+ signals by simultaneous multi-focal imaging

Elementary events such as puffs and sparks are cytosolic microdomains of Ca2+ from which cellular Ca2+ signals are constructed. Because of the tight localization and fast kinetics of elementary events, imaging studies have been hindered by instrumental limitations of confocal and deconvolution fluorescence microscopy which necessitate compromises between spatial and temporal resolution. Here, we describe a novel, yet simple 'multi-focal' fluorescence microscopy system that employs three high-speed cameras focused at different axial depths to enable 4-dimensional imaging with millisecond resolution. We demonstrate the utility of this system for studies of puffs in Xenopus oocytes by mapping the axial distribution of puff sites, by obtaining measurements of puff amplitudes undistorted by focus error, and by deriving deblurred images that reveal novel sub-micron jumps of Ca2+ release sites.

Lipid rafts establish calcium waves in hepatocytes

BACKGROUND & AIMS

Polarity is critical for hepatocyte function. Ca(2+) waves are polarized in hepatocytes because the inositol 1,4,5-trisphosphate receptor (InsP3R) is concentrated in the pericanalicular region, but the basis for this localization is unknown. We examined whether pericanalicular localization of the InsP3R and its action to trigger Ca(2+) waves depends on lipid rafts.

METHODS

Experiments were performed using isolated rat hepatocyte couplets and pancreatic acini, plus SkHep1 cells as nonpolarized controls. The cholesterol depleting agent methyl-beta-cyclodextrin (mbetaCD) was used to disrupt lipid rafts. InsP3R isoforms were examined by immunoblot and immunofluorescence. Ca(2+) waves were examined by confocal microscopy.

RESULTS

Type II InsP3Rs initially were localized to only some endoplasmic reticulum fractions in hepatocytes, but redistributed into all fractions in mbetaCD-treated cells. This InsP3R isoform was concentrated in the pericanalicular region, but redistributed throughout the cell after mbetaCD treatment. Vasopressin-induced Ca(2+) signals began as apical-to-basal Ca(2+) waves, and mbetaCD slowed the wave speed and prolonged the rise time. MbetaCD had a similar effect on Ca(2+) waves in acinar cells but did not affect Ca(2+) signals in SkHep1 cells, suggesting that cholesterol depletion has similar effects among polarized epithelia, but this is not a nonspecific effect of mbetaCD.

CONCLUSIONS

Lipid rafts are responsible for the pericanalicular accumulation of InsP3R in hepatocytes, and for the polarized Ca(2+) waves that result. Signaling microdomains exist not only in the plasma membrane, but also in the nearby endoplasmic reticulum, which in turn, helps establish and maintain structural and functional polarity.

A kinetic model of single and clustered IP3 receptors in the absence of Ca2+ feedback

Ca2+ liberation through inositol 1,4,5-trisphosphate receptor (IP3R) channels generates complex patterns of spatiotemporal cellular Ca2+ signals owing to the biphasic modulation of channel gating by Ca2+ itself. These processes have been extensively studied in Xenopus oocytes, where imaging studies have revealed local Ca2+ signals ("puffs") arising from clusters of IP3R, and patch-clamp studies on isolated oocyte nuclei have yielded extensive data on IP3R gating kinetics. To bridge these two levels of experimental data, we developed an IP3R model and applied stochastic simulation and transition matrix theory to predict the behavior of individual and clustered IP3R channels. The channel model consists of four identical, independent subunits, each of which has an IP3-binding site together with one activating and one inactivating Ca2+-binding site. The channel opens when at least three subunits undergo a conformational change to an "active" state after binding IP3 and Ca2+. The model successfully reproduces patch-clamp data; including the dependence of open probability, mean open duration, and mean closed duration on [IP3] and [Ca2+]. Notably, the biexponential distribution of open-time duration and the dependence of mean open time on [Ca2+] are explained by populations of openings involving either three or four active subunits. As a first step toward applying the single IP3R model to describe cellular responses, we then simulated measurements of puff latency after step increases of [IP3]. Assuming that stochastic opening of a single IP3R at basal cytosolic [Ca2+] and any given [IP3] has a high probability of rapidly triggering neighboring channels by calcium-induced calcium release to evoke a puff, optimal correspondence with experimental data of puff latencies after photorelease of IP3 was obtained when the cluster contained a total of 40-70 IP3Rs.

Pacemaking through Ca2+ stores interacting as coupled oscillators via membrane depolarization

This study presents an investigation of pacemaker mechanisms underlying lymphatic vasomotion. We tested the hypothesis that active inositol 1,4,5-trisphosphate receptor (IP(3)R)-operated Ca(2+) stores interact as coupled oscillators to produce near-synchronous Ca(2+) release events and associated pacemaker potentials, this driving action potentials and constrictions of lymphatic smooth muscle. Application of endothelin 1 (ET-1), an agonist known to enhance synthesis of IP(3), to quiescent lymphatic smooth muscle syncytia first enhanced spontaneous Ca(2+) transients and/or intracellular Ca(2+) waves. Larger near-synchronous Ca(2+) transients then occurred leading to global synchronous Ca(2+) transients associated with action potentials and resultant vasomotion. In contrast, blockade of L-type Ca(2+) channels with nifedipine prevented ET-1 from inducing near-synchronous Ca(2+) transients and resultant action potentials, leaving only asynchronous Ca(2+) transients and local Ca(2+) waves. These data were well simulated by a model of lymphatic smooth muscle with: 1), oscillatory Ca(2+) release from IP(3)R-operated Ca(2+) stores, which causes depolarization; 2), L-type Ca(2+) channels; and 3), gap junctions between cells. Stimulation of the stores caused global pacemaker activity through coupled oscillator-based entrainment of the stores. Membrane potential changes and positive feedback by L-type Ca(2+) channels to produce more store activity were fundamental to this process providing long-range electrochemical coupling between the Ca(2+) store oscillators. We conclude that lymphatic pacemaking is mediated by coupled oscillator-based interactions between active Ca(2+) stores. These are weakly coupled by inter- and intracellular diffusion of store activators and strongly coupled by membrane potential. Ca(2+) store-based pacemaking is predicted for cellular systems where: 1), oscillatory Ca(2+) release induces depolarization; 2), membrane depolarization provides positive feedback to induce further store Ca(2+) release; and 3), cells are interconnected. These conditions are met in a surprisingly large number of cellular systems including gastrointestinal, lymphatic, urethral, and vascular tissues, and in heart pacemaker cells.

The spatial distribution of inositol 1,4,5-trisphosphate receptor isoforms shapes Ca2+ waves

Cytosolic Ca(2+) is a versatile second messenger that can regulate multiple cellular processes simultaneously. This is accomplished in part through Ca(2+) waves and other spatial patterns of Ca(2+) signals. To investigate the mechanism responsible for the formation of Ca(2+) waves, we examined the role of inositol 1,4,5-trisphosphate receptor (InsP3R) isoforms in Ca(2+) wave formation. Ca(2+) signals were examined in hepatocytes, which express the type I and II InsP3R in a polarized fashion, and in AR4-2J cells, a nonpolarized cell line that expresses type I and II InsP3R in a ratio similar to what is found in hepatocytes but homogeneously throughout the cell. Expression of type I or II InsP3R was selectively suppressed by isoform-specific DNA antisense in an adenoviral delivery system, which was delivered to AR4-2J cells in culture and to hepatocytes in vivo. Loss of either isoform inhibited Ca(2+) signals to a similar extent in AR4-2J cells. In contrast, loss of the basolateral type I InsP3R decreased the sensitivity of hepatocytes to vasopressin but had little effect on the initiation or spread of Ca(2+) waves across hepatocytes. Loss of the apical type II isoform caused an even greater decrease in the sensitivity of hepatocytes to vasopressin and resulted in Ca(2+) waves that were much slower and delayed in onset. These findings provide evidence that the apical concentration of type II InsP3Rs is essential for the formation of Ca(2+) waves in hepatocytes. The subcellular distribution of InsP3R isoforms may critically determine the repertoire of spatial patterns of Ca(2+) signals.

Characterization of local calcium signals in tubular networks of endoplasmic reticulum

To explain the large time and space scales of elementary calcium events in Xenopus oocytes it is assumed that the Ca2+ source is located on tubules of the endoplasmic reticulum, which provide local barriers for diffusion. The event duration, width and signal mass dependence on the total quantity of released Ca2+ is determined at different orientations of the scan line and different ionic currents. Excellent agreement with published data is obtained with on- and off-rate constants of the fluorescent indicator of 15 microM(-1) s(-1) and 2.55 s(-1), respectively. It is found that one signal mass unit, calculated with the classical method that assumes spherical symmetry of the cytosolic space surrounding the release site, corresponds to 0.189 fC of released Ca2+ in the presence of a tubular network. It is estimated that release Ca2+ currents and amounts are randomly distributed, with averages of 0.165 pA and 3.66 fC per event and average release duration of 22.2 ms. The total quantity of liberated Ca2+ and the release current amplitude in the presence of endoplasmic reticulum tubules is predicted to be about one order of magnitude lower than estimated within the isotropic diffusion formalism. This could have implications in muscle cell Ca2+ imaging as well.

Astrocyte calcium waves: what they are and what they do

Several lines of evidence indicate that the elaborated calcium signals and the occurrence of calcium waves in astrocytes provide these cells with a specific form of excitability. The identification of the cellular and molecular steps involved in the triggering and transmission of Ca(2+) waves between astrocytes resulted in the identification of two pathways mediating this form of intercellular communication. One of them involves the direct communication between the cytosols of two adjoining cells through gap junction channels, while the other depends upon the release of "gliotransmitters" that activates membrane receptors on neighboring cells. In this review we summarize evidence in favor of these two mechanisms of Ca(2+) wave transmission and we discuss that they may not be mutually exclusive, but are likely to work in conjunction to coordinate the activity of a group of cells. To address a key question regarding the functional consequences following the passage of a Ca(2+) wave, we list, in this review, some of the potential intracellular targets of these Ca(2+) transients in astrocytes, and discuss the functional consequences of the activation of these targets for the interactions that astrocytes maintain with themselves and with other cellular partners, including those at the glial/vasculature interface and at perisynaptic sites where astrocytic processes tightly interact with neurons.

Ca2+ microdomains in smooth muscle

In smooth muscle, Ca(2+) controls diverse activities including cell division, contraction and cell death. Of particular significance in enabling Ca(2+) to perform these multiple functions is the cell's ability to localize Ca(2+) signals to certain regions by creating high local concentrations of Ca(2+) (microdomains), which differ from the cytoplasmic average. Microdomains arise from Ca(2+) influx across the plasma membrane or release from the sarcoplasmic reticulum (SR) Ca(2+) store. A single Ca(2+) channel can create a microdomain of several micromolar near (approximately 200 nm) the channel. This concentration declines quickly with peak rates of several thousand micromolar per second when influx ends. The high [Ca(2+)] and the rapid rates of decline target Ca(2+) signals to effectors in the microdomain with rapid kinetics and enable the selective activation of cellular processes. Several elements within the cell combine to enable microdomains to develop. These include the brief open time of ion channels, localization of Ca(2+) by buffering, the clustering of ion channels to certain regions of the cell and the presence of membrane barriers, which restrict the free diffusion of Ca(2+). In this review, the generation of microdomains arising from Ca(2+) influx across the plasma membrane and the release of the ion from the SR Ca(2+) store will be discussed and the contribution of mitochondria and the Golgi apparatus as well as endogenous modulators (e.g. cADPR and channel binding proteins) will be considered.

Calcium microdomains and oxidative stress

The phenomenon of calcium microdomains is firmly established in the field of subcellular physiology. These regions of localized, transient calcium increase are exemplified by the spontaneous 'sparks' released through the ryanodine receptor in myocytes, but include subplasmalemmal microdomains, focal calcium oscillations and microdomains enclosed within organelles, such as the endoplasmic reticulum, golgi and mitochondria. Increasing evidence suggests that oxidative stress regulates both the formation and disappearance of microdomains. Calcium release channels and transporters are all modulated by redox state, while several mechanisms that generate oxidative or nitrosative stress are regulated by calcium. Here, we discuss the evidence for the regulation of calcium microdomains by redox state, and, by way of example, demonstrate that the frequency of calcium sparks in cardiomyocytes is increased in response to oxidative stress. We consider the evidence for the existence of analogous microdomains of reactive oxygen and nitrogen species and suggest that the refinement of imaging techniques for these species might lead to similar concepts. The interaction between Ca(2+) microdomains and proteins that modulate their formation results in a complex and dynamic, spatial signaling mechanism, which is likely to be broadly applicable to different cell types, adding new dimensions to the calcium signaling 'toolkit'.

'Trigger' events precede calcium puffs in Xenopus oocytes

The liberation of calcium ions sequestered in the endoplasmic reticulum through inositol 1,4,5-trisphosphate receptors/channels (IP(3)Rs) results in a spatiotemporal hierarchy of calcium signaling events that range from single-channel openings to local Ca(2+) puffs believed to arise from several to tens of clustered IP(3)Rs to global calcium waves. Using high-resolution confocal linescan imaging and a sensitive Ca(2+) indicator dye (fluo-4-dextran), we show that puffs are often preceded by small, transient Ca(2+) elevations that we christen "trigger events". The magnitude of triggers is consistent with their arising from the opening of a single IP(3) receptor/channel, and we propose that they initiate puffs by recruiting neighboring IP(3)Rs within the cluster by a regenerative process of Ca(2+)-induced Ca(2+) release. Puff amplitudes (fluorescence ratio change) are on average approximately 6 times greater than that of the triggers, suggesting that at least six IP(3)Rs may simultaneously be open during a puff. Trigger events have average durations of approximately 12 ms, as compared to 19 ms for the mean rise time of puffs, and their spatial extent is approximately 3 times smaller than puffs (respective widths at half peak amplitude 0.6 and 1.6 micro m). All these parameters were relatively independent of IP(3) concentration, although the proportion of puffs showing resolved triggers was greatest (approximately 80%) at low [IP(3)]. Because Ca(2+) puffs constitute the building blocks from which cellular IP(3)-mediated Ca(2+) signals are constructed, the events that initiate them are likely to be of fundamental importance for cell signaling. Moreover, the trigger events provide a useful yardstick by which to derive information regarding the number and spatial arrangement of IP(3)Rs within clusters.

The number and spatial distribution of IP3 receptors underlying calcium puffs in Xenopus oocytes

Calcium puffs are local Ca(2+) release events that arise from a cluster of inositol 1,4,5-trisphosphate receptor channels (IP(3)Rs) and serve as a basic "building block" from which global Ca(2+) waves are generated. Important questions remain as to the number of IP(3)Rs that open during a puff, their spatial distribution within a cluster, and how much Ca(2+) current flows through each channel. The recent discovery of "trigger" events-small Ca(2+) signals that immediately precede puffs and are interpreted to arise through opening of single IP(3)R channels-now provides a useful yardstick by which to calibrate the Ca(2+) flux underlying puffs. Here, we describe a deterministic numerical model to simulate puffs and trigger events. Based on confocal linescan imaging in Xenopus oocytes, we simulated Ca(2+) release in two sequential stages; representing the trigger by the opening of a single IP(3)R in the center of a cluster for 12 ms, followed by the concerted opening of some number of IP(3)Rs for 19 ms, representing the rising phase of the puff. The diffusion of Ca(2+) and Ca(2+)-bound indicator dye were modeled in a three-dimensional cytosolic volume in the presence of immobile and mobile Ca(2+) buffers, and were used to predict the observed fluorescence signal after blurring by the microscope point-spread function. Optimal correspondence with experimental measurements of puff spatial width and puff/trigger amplitude ratio was obtained assuming that puffs arise from the synchronous opening of 25-35 IP(3)Rs, each carrying a Ca(2+) current of approximately 0.4 pA, with the channels distributed through a cluster 300-800 nm in diameter.

Cytosolic inositol 1,4,5-trisphosphate dynamics during intracellular calcium oscillations in living cells

We developed genetically encoded fluorescent inositol 1,4,5-trisphosphate (IP₃) sensors that do not severely interfere with intracellular Ca²⁺ dynamics and used them to monitor the spatiotemporal dynamics of both cytosolic IP₃ and Ca²⁺ in single HeLa cells after stimulation of exogenously expressed metabotropic glutamate receptor 5a or endogenous histamine receptors. IP₃ started to increase at a relatively constant rate before the pacemaker Ca²⁺ rise, and the subsequent abrupt Ca²⁺ rise was not accompanied by any acceleration in the rate of increase in IP₃. Cytosolic [IP₃] did not return to its basal level during the intervals between Ca²⁺ spikes, and IP₃ gradually accumulated in the cytosol with a little or no fluctuations during cytosolic Ca²⁺ oscillations. These results indicate that the Ca²⁺-induced regenerative IP₃ production is not a driving force of the upstroke of Ca²⁺ spikes and that the apparent IP₃ sensitivity for Ca²⁺ spike generation progressively decreases during Ca²⁺ oscillations.

Signaling proteins in raft-like microdomains are essential for Ca2+ wave propagation in glial cells

The hypothesis that calcium signaling proteins segregate into lipid raft-like microdomains was tested in isolated membranes of rat oligodendrocyte progenitor (OP) cells and astrocytes using Triton X-100 solubilization and density gradient centrifugation. Western blot analysis of gradient fractions showed co-localization of caveolin-1 with proteins involved in the Ca2+ signaling cascade. These included agonist receptors, P2Y1, and M1, TRPC1, IP3R2, ryanodine receptor, as well as the G protein Galphaq and Homer. Membranes isolated from agonist-stimulated astrocytes showed an enhanced recruitment of phospholipase C (PLCbeta1), IP3R2 and protein kinase C (PKC-alpha) into lipid raft fractions. IP3R2, TRPC1 and Homer co-immunoprecipitated, suggesting protein-protein interactions. Disruption of rafts by cholesterol depletion using methyl-beta-cyclodextrin (beta-MCD) altered the distribution of caveolin-1 and GM1 to non-raft fractions with higher densities. beta-MCD-induced disruption of rafts inhibited agonist-evoked Ca2+ wave propagation in astrocytes and attenuated wave speeds. These results indicate that in glial cells, Ca2+ signaling proteins might exist in organized membrane microdomains, and these complexes may include proteins from different cellular membrane systems. Such an organization is essential for Ca2+ wave propagation.

PKCalpha: a versatile key for decoding the cellular calcium toolkit

Conventional protein kinases C (cPKCs) play an essential role in signal transduction and are believed to integrate both global Ca²⁺ transients and diacylglycerol signals. We provide evidence that PKCα is a ubiquitous readout sensor for the cellular Ca²⁺ toolkit, including highly restricted elementary Ca²⁺ release.

Threshold stimulations of cells with Ca²⁺-mobilizing agonists resulted in PKCα translocation events with limited spatial spreads (<4 μm) comprising two groups of lifetimes; brief events (400–1,500 ms) exclusively mediated by Ca²⁺–C2 domain membrane interactions and long-lasting events (>4 s) resulting from longer DAG-C1a domain–mediated membrane interactions.

Although upon uncaging NP-EGTA, which is a caged Ca²⁺ compound, WT-PKCα displayed rapid membrane translocations within <250 ms, PKCα constructs with C2 domains mutated in their Ca²⁺-binding region lacked any Ca²⁺-dependent translocation. Flash photolysis of diazo-2, a photosensitive caged Ca²⁺ buffer, revealed a biphasic membrane dissociation (slow and fast period) of WT-PKCα. The slow phase was absent in cells expressing PKCα-constructs containing mutated C1a-domains with largely reduced DAG binding. Thus, two groups of PKCα membrane interactions coexist; C2- and C1a-mediated interactions with different lifetimes but rapid interconversion.

We conclude that PKCα can readout very fast and, spatially and temporally, very complex cellular Ca²⁺ signals. Therefore, cPKCs are important transducers for the ubiquitous cellular Ca²⁺ signaling toolkit.

Cytoplasmic Ca2+ signals and cellular death by apoptosis in myocardiac H9c2 cells

The incubation of H9c2 cells with 10 microM thapsigargin (TG) was associated with the appearance of a two-component cytoplasmic Ca2+ peak. Experiments performed in a Ca2+-free medium indicated that both components came from intracellular sources. The first component of the signal corresponded to the discharge of the sarco-endoplasmic reticulum (SER) Ca2+ store. The appearance of the second component was prevented by cell preincubation with cyclosporin A (CsA) and gave rise to a clear and permanent depolarization of the mitochondrial inner membrane. These features were indication of a mitochondrial origin. The observed release of mitochondrial Ca2+ was related with opening of the permeability transition pore (PTP). The two-component cytoplasmic Ca2+ peak, i.e., treatment with 10 microM TG, as compared with the first component alone, i.e., treatment with 3 microM TG, was associated with a faster process of cellular death. In both cases, chromatin fragmentation and condensation at the nuclear periphery were observed. Other prominent apoptotic events such as loss of DNA content and cleavage of poly(ADP-ribose) polymerase (PARP) were also dependent on TG concentration and occurred in different time windows. PTP opening induced by 10 microM TG was responsible for the faster apoptotic death.

Requirement for a localized, IP3R-generated Ca2+transient during the furrow positioning process in zebrafish zygotes

We report that the first localized Ca2+transient visualized in the blastodisc cortex of post-mitotic zebrafish zygotes has unique features. We confirm that this initial ‘furrow positioning’ Ca2+transient precedes the physical appearance of the first cleavage furrow at the blastodisc surface and that it has unique dynamics, which distinguish it from the subsequent furrow propagation transients that develop from it. This initial transient displays a distinct rising phase that peaks prior to the initiation of the two linear, subsurface, self-propagating Ca2+waves that constitute the subsequent furrow propagation transient. Through the carefully timed introduction of the Ca2+buffer, dibromo-BAPTA, we also demonstrate the absolute requirement of this initial rising phase Ca2+transient in positioning the furrow at the blastodisc surface: no rising phase transient, no cleavage furrow. Likewise, the introduction of the inositol 1,4,5-trisphosphate receptor (IP3R) antagonist, 2-aminoethoxydiphenyl borate, eliminates both the rising phase transient and the appearance of the furrow at the cell surface. On the other hand, antagonists of the ryanodine receptor and NAADP-sensitive channels, or simply bathing the zygote in Ca2+-free medium, have no effect on the generation of the rising phase positioning transient or the appearance of the furrow at the surface. This suggests that like the subsequent propagation and deepening/zipping Ca2+transients, the rising phase furrow positioning transient is also generated specifically by Ca2+released via IP3Rs. We propose, however, that despite being generated by a similar Ca2+release mechanism, the unique features of this initial transient suggest that it might be a distinct signal with a specific function associated with positioning the cleavage furrow at the blastodisc surface.

Graded recruitment and inactivation of single InsP3 receptor Ca2+-release channels: implications for quantal [corrected] Ca2+release

Modulation of cytoplasmic free Ca2+ concentration ([Ca2+]i) by receptor-mediated generation of inositol 1,4,5-trisphosphate (InsP3) and activation of its receptor (InsP3R), a Ca2+-release channel in the endoplasmic reticulum, is a ubiquitous signalling mechanism. A fundamental aspect of InsP3-mediated signalling is the graded release of Ca2+ in response to incremental levels of stimuli. Ca2+ release has a transient fast phase, whose rate is proportional to [InsP3], followed by a much slower one even in constant [InsP3]. Many schemes have been proposed to account for quantal Ca2+ release, including the presence of heterogeneous channels and Ca2+ stores with various mechanisms of release termination. Here, we demonstrate that mechanisms intrinsic to the single InsP3R channel can account for quantal Ca2+ release. Patch-clamp electrophysiology of isolated insect Sf9 cell nuclei revealed a consistent and high probability of detecting functional endogenous InsP3R channels, enabling InsP3-induced channel inactivation to be identified as an inevitable consequence of activation, and allowing the average number of activated channels in the membrane patch (N(A)) to be accurately quantified. InsP3-activated channels invariably inactivated, with average duration of channel activity reduced by high [Ca2+]i and suboptimal [InsP3]. Unexpectedly, N(A) was found to be a graded function of both [Ca2+]i and [InsP3]. A qualitative model involving Ca2+-induced InsP3R sequestration and inactivation can account for these observations. These results suggest that apparent heterogeneous ligand sensitivity can be generated in a homogeneous population of InsP3R channels, providing a mechanism for graded Ca2+ release that is intrinsic to the InsP3R Ca2+ release channel itself.

Analysis of puff dynamics in oocytes: interdependence of puff amplitude and interpuff interval

Puffs are localized Ca(2+) signals that arise in oocytes in response to inositol 1,4,5-trisphosphate (IP(3)). They are analogous to the sparks of myocytes and are believed to be the result of the liberation of Ca(2+) from the endoplasmic reticulum through the coordinated opening of IP(3) receptor/channels clustered at a functional release site. In this article, we analyze sequences of puffs that occur at the same site to help elucidate the mechanisms underlying puff dynamics. In particular, we show a dependence of the interpuff time on the amplitude of the preceding puff, and of the amplitude of the following puff on the preceding interval. These relationships can be accounted for by an inhibitory role of the Ca(2+) that is liberated during puffs. We construct a stochastic model for a cluster of IP(3) receptor/channels that quantitatively replicates the observed behavior, and we determine that the characteristic time for a channel to escape from the inhibitory state is of the order of seconds.

Modeling the statistics of elementary calcium release events

Elementary Ca(2+) signals, such as "Ca(2+) puffs", which arise from the release of Ca(2+) from endoplasmic reticulum through small clusters of inositol 1,4,5-trisphosphate receptors, are the building blocks for intracellular Ca(2+) signaling. The small number of release channels involved during a Ca(2+) puff renders the puffs stochastic, with distributed amplitudes, durations, and frequency, well characterized experimentally. We present a stochastic model that accurately describes simultaneously the statistical properties of the duration, amplitudes, frequencies, and spatial spread with a single set of parameters.

Microdomains of intracellular Ca2+: molecular determinants and functional consequences

Calcium ions are ubiquitous and versatile signaling molecules, capable of decoding a variety of extracellular stimuli (hormones, neurotransmitters, growth factors, etc.) into markedly different intracellular actions, ranging from contraction to secretion, from proliferation to cell death. The key to this pleiotropic role is the complex spatiotemporal organization of the [Ca(2+)] rise evoked by extracellular agonists, which allows selected effectors to be recruited and specific actions to be initiated. In this review, we discuss the structural and functional bases that generate the subcellular heterogeneity in cellular Ca(2+) levels at rest and under stimulation. This complex choreography requires the concerted action of many different players; the central role is, of course, that of the calcium ion, with the main supporting characters being all the entities responsible for moving Ca(2+) between different compartments, while the cellular architecture provides a determining framework within which all the players have their exits and their entrances. In particular, we concentrate on the molecular mechanisms that lead to the generation of cytoplasmic Ca(2+) microdomains, focusing on their different subcellular location, mechanism of generation, and functional role.

Models of the inositol trisphosphate receptor

The inositol (1,4,5)-trisphosphate receptor (IPR) plays a crucial role in calcium dynamics in a wide range of cell types, and is often a central feature in quantitative models of calcium oscillations and waves. We review deterministic and stochastic mathematical models of the IPR, from the earliest ones of the 1970s and 1980s, to the most recent. The effects of IPR stochasticity on Ca2+ dynamics are briefly discussed.

Local calcium transients contribute to disappearance of pFAK, focal complex removal and deadhesion of neuronal growth cones and fibroblasts

Cell adhesion is crucial for migration of cells during development, and cell-substrate adhesion of motile cells is accomplished through the formation and removal of focal complexes that are sites of cell-substrate contact. Because Ca2+ signaling regulates the rate of axon outgrowth and growth cone turning, we investigated the potential role of Ca2+ in focal complex dynamics. We describe a novel class of localized, spontaneous transient elevations of cytosolic Ca2+ observed both in Xenopus neuronal growth cones and fibroblasts that are 2-6 mum in spatial extent and 2-4 s in duration. They are distributed throughout growth cone lamellipodia and at the periphery of fibroblast pseudopodia, which are regions of high motility. In both cell types, these Ca2+ transients lead to disappearance of phosphorylated focal adhesion kinase (pFAK) and deadhesion from the substrate as assessed by confocal and internal reflection microscopy, respectively. The loss of pFAK is inhibited by cyclosporin A, suggesting that these Ca2+ transients exert their effects via calcineurin. These results identify an intrinsic mechanism for local cell detachment that may be modulated by agents that regulate motility.

The dynamics of stochastic attrition viewed as an absorption time on a terminating Markov chain

Localized Ca(2+) elevations known as Ca(2+) puffs and sparks are cellular signals that arise from the cooperative activity of clusters of inositol 1,4,5-trisphosphate receptors and ryanodine receptors clustered at Ca(2+) release sites on the surface of the endoplasmic reticulum or sarcoplasmic reticulum. When Markov chain models of these intracellular Ca(2+)-regulated Ca(2+) channels are coupled via a mathematical representation of Ca(2+) microdomain, simulated Ca(2+) release sites may exhibit the phenomenon of "stochastic Ca(2+) excitability" where the inositol 1,4,5-trisphosphate receptors (IP(3)Rs) or ryanodine receptors (RyRs) open and close in a concerted fashion. Interestingly, under some conditions simulated puffs and sparks can be observed even when the single-channel model used does not include slow Ca(2+) inactivation or, indeed, any long-lived closed/refractory state [V. Nguyen, R. Mathias, G. Smith, Stochastic automata network descriptor for Markov chain models of instantaneously-coupled intracellular Ca(2+) channels, Bull. Math. Biol. 67 (2005) 393-432]. In this case, termination of the localized Ca(2+) elevation occurs when all of the intracellular channels at a release site simultaneously close through a process referred to as stochastic attrition [M. Stern, Theory of excitation-contraction coupling in cardiac muscle, Biophys. J. 63 (1992) 497-517]. In this paper, we investigate the statistical properties of stochastic attrition viewed as an absorption time on a terminating Markov chain that represents a Ca(2+) release site composed of N two-state channels that are activated by Ca(2+). Assuming that the local [Ca(2+)] experienced by a channel depends only on the number of open channels at the Ca(2+) release site (i.e., instantaneous mean-field coupling [ibid.], we derive the probability distribution function for the time until stochastic attrition occurs and present an analytical formula for the expectation of this random variable. We explore how the contribution of stochastic attrition to the termination of Ca(2+) puffs and sparks depends on the number of channels at a release site, the source amplitude of the channels (i.e., the strength of the coupling), the background [Ca(2+)], channel kinetics, and the cooperactivity of Ca(2+) binding. Because we explicitly model the Ca(2+) regulation of the intracellular channels, our results differ markedly from (and in fact generalize) preliminary analyses that assume the intracellular Ca(2+) channels are uncoupled and consequently independent.

Reactive clusters on a membrane

We investigate the reaction dynamics of diffusive molecules with immobile binding partners. The fixed reactants build clusters that are comprised of just a few tens of molecules, which leads to small cluster sizes. These molecules participate in the reaction only if they are activated. The dynamics of activation is mapped to a time-dependent size of an active region within the cluster. We focus on the deterministic description of the dynamics of a single cluster. The spatial setup accounts for one of the most important determinants of the dynamics of a cluster, i.e. diffusional transport of reaction partners towards or away from the active region of the cluster. We provide numerical and analytical evidence that diffusion influences decisively the dynamic regimes of the reactions. The application of our methods to intracellular Ca2+ dynamics shows that large local concentrations saturate the Ca2+ feedback to the channel state control. It eliminates oscillations depending on this feedback.

UNLOCKING THE SECRETS OF CELL SIGNALING

My scientific life has been spent trying to understand how cells communicate with each other. This interest in cell signaling began with studies on the control of fluid secretion by an insect salivary gland, and the subsequent quest led to the discovery of inositol trisphosphate (IP3) and its role in calcium signaling, which effectively divided my scientific career into two distinct parts. The first part was primarily experimental and culminated in the discovery of IP3, which set the agenda for the second half during which I have enjoyed exploring the many functions of this remarkably versatile signaling system. It has been particularly exciting to find out how this IP3/Ca2+ signaling pathway has been adapted to control processes as diverse as fertilization, proliferation, cell contraction, secretion, and information processing in neuronal cells.

Molecular Cloning of Mouse Type 2 and Type 3 Inositol 1,4,5-Trisphosphate Receptors and Identification of a Novel Type 2 Receptor Splice Variant

We isolated cDNAs encoding type 2 and type 3 inositol 1,4,5-trisphosphate (IP(3)) receptors (IP(3)R2 and IP(3)R3, respectively) from mouse lung and found a novel alternative splicing segment, SI(m2), at 176-208 of IP(3)R2. The long form (IP(3)R2 SI(m2)(+)) was dominant, but the short form (IP(3)R2 SI(m2)(-)) was detected in all tissues examined. IP(3)R2 SI(m2)(-) has neither IP(3) binding activity nor Ca(2+) releasing activity. In addition to its reticular distribution, IP(3)R2 SI(m2)(+) is present in the form of clusters in the endoplasmic reticulum of resting COS-7 cells, and after ATP or Ca(2+) ionophore stimulation, most of the IP(3)R2 SI(m2)(+) is in clusters. IP(3)R3 is localized uniformly on the endoplasmic reticulum of resting cells and forms clusters after ATP or Ca(2+) ionophore stimulation. IP(3)R2 SI(m2)(-) does not form clusters in either resting or stimulated cells. IP(3) binding-deficient site-directed mutants of IP(3)R2 SI(m2)(+) and IP(3)R3 fail to form clusters, indicating that IP(3) binding is involved in the cluster formation by these isoforms. Coexpression of IP(3)R2 SI(m2)(-) prevents stimulus-induced IP(3)R clustering, suggesting that IP(3)R2 SI(m2)(-) functions as a negative coordinator of stimulus-induced IP(3)R clustering. Expression of IP(3)R2 SI(m2)(-) in CHO-K1 cells significantly reduced ATP-induced Ca(2+) entry, but not Ca(2+) release, suggesting that the novel splice variant of IP(3)R2 specifically influences the dynamics of the sustained phase of Ca(2+) signals.

Ca2+ blinks: rapid nanoscopic store calcium signaling

Luminal Ca(2+) in the endoplasmic and sarcoplasmic reticulum (ER/SR) plays an important role in regulating vital biological processes, including store-operated capacitative Ca(2+) entry, Ca(2+)-induced Ca(2+) release, and ER/SR stress-mediated cell death. We report rapid and substantial decreases in luminal [Ca(2+)], called "Ca(2+) blinks," within nanometer-sized stores (the junctional cisternae of the SR) during elementary Ca(2+) release events in heart cells. Blinks mirror small local increases in cytoplasmic Ca(2+),orCa(2+) sparks, but changes of [Ca(2+)] in the connected free SR network were below detection. Store microanatomy suggests that diffusional strictures may account for this paradox. Surprisingly, the nadir of the store depletion trails the peak of the spark by about 10 ms, and the refilling of local store occurs with a rate constant of 35 s(-1), which is approximately 6-fold faster than the recovery of local Ca(2+) release after a spark. These data suggest that both local store depletion and some time-dependent inhibitory mechanism contribute to spark termination and refractoriness. Visualization of local store Ca(2+) signaling thus broadens our understanding of cardiac store Ca(2+) regulation and function and opens the possibility for local regulation of diverse store-dependent functions.

A model-independent algorithm to derive Ca2+ fluxes underlying local cytosolic Ca2+ transients

Local intracellular Ca(2+) signals result from Ca(2+) flux into the cytosol through individual channels or clusters of channels. To gain a mechanistic understanding of these events we need to know the magnitude and spatial distribution of the underlying Ca(2+) flux. However, this is difficult to infer from fluorescence Ca(2+) images because the distribution of Ca(2+)-bound dye is affected by poorly characterized processes including diffusion of Ca(2+) ions, their binding to mobile and immobile buffers, and sequestration by Ca(2+) pumps. Several methods have previously been proposed to derive Ca(2+) flux from fluorescence images, but all require explicit knowledge or assumptions regarding these processes. We now present a novel algorithm that requires few assumptions and is largely model-independent. By testing the algorithm with both numerically generated image data and experimental images of sparklets resulting from Ca(2+) flux through individual voltage-gated channels, we show that it satisfactorily reconstructs the magnitude and time course of the underlying Ca(2+) currents.

Stability of membrane bound reactions

We present a novel approach to the dynamics of reactions of diffusing chemical species with species fixed in space, e.g., by binding to a membrane. The nondiffusing reaction partners are clustered in areas with a diameter smaller than the diffusion length of the diffusing partner. The activated fraction of the fixed species determines the size of an active subregion of the cluster. Linear stability analysis reveals that diffusion is one of the major determinants of the stability of the dynamics. We illustrate the model concept with Ca2+ dynamics in living cells, which has release channels as fixed reaction partners. Our results suggest that spatial and temporal structures in intracellular Ca2+ dynamics are caused by fluctuations due to the small number of channels per cluster.

Imaging microdomain Ca2+ in muscle cells

Ca2+ ions passing through a single or a cluster of Ca2+-permeable channels create microscopic, short-lived Ca2+ gradients that constitute the building blocks of cellular Ca2+ signaling. Over the last decade, imaging microdomain Ca2+ in muscle cells has unveiled the exquisite spatial and temporal architecture of intracellular Ca2+ dynamics and has reshaped our understanding of Ca2+ signaling mechanisms. Major advances include the visualization of "Ca2+ sparks" as the elementary events of Ca2+ release from the sarcoplasmic reticulum (SR), "Ca2+ sparklets" produced by openings of single Ca2+-permeable channels, miniature Ca2+ transients in single mitochondria ("marks"), and SR luminal Ca2+ depletion transients ("scraps"). As a model system, a cardiac myocyte contains a 3-dimensional grid of 104 spark ignition sites, stochastic activation of which summates into global Ca2+ transients. Tracking intermolecular coupling between single L-type Ca2+ channels and Ca2+ sparks has provided direct evidence validating the local control theory of Ca2+-induced Ca2+ release in the heart. In vascular smooth muscle myocytes, Ca2+ can paradoxically signal both vessel constriction (by global Ca2+ transients) and relaxation (by subsurface Ca2+ sparks). These findings shed new light on the origin of Ca2+ signaling efficiency, specificity, and versatility. In addition, microdomain Ca2+ imaging offers a novel modality that complements electrophysiological approaches in characterizing Ca2+ channels in intact cells.

Peripheral hot spots for local Ca2+ release after single action potentials in sympathetic ganglion neurons

Ca2+ release from the endoplasmic reticulum (ER) contributes to Ca2+ transients in frog sympathetic ganglion neurons. Here we use video-rate confocal fluo-4 fluorescence imaging to show that single action potentials reproducibly trigger rapidly rising Ca2+ transients at 1-3 local hot spots within the peripheral ER-rich layer in intact neurons in fresh ganglia and in the majority (74%) of cultured neurons. Hot spots were located near the nucleus or the axon hillock region. Other regions exhibited either slower and smaller signals or no response. Ca2+ signals spread into the cell at constant velocity across the ER in nonnuclear regions, indicating active propagation, but spread with a (time)1/2 dependence within the nucleus, consistent with diffusion. 26% of cultured cells exhibited uniform Ca2+ signals around the periphery, but hot spots were produced by loading the cytosol with EGTA or by bathing such cells in low-Ca2+ Ringer's solution. Peripheral hot spots for Ca2+ release within the perinuclear and axon hillock regions provide a mechanism for preferential initiation of nuclear and axonal Ca2+ signals by single action potentials in sympathetic ganglion neurons.

Saltatory and continuous calcium waves and the rapid buffering approximation

Calcium waves propagate inside cells due to a regenerative mechanism known as calcium-induced calcium release. Buffer-mediated calcium diffusion in the cytosol plays a crucial role in the process. However, most models of calcium waves either treat buffers phenomenologically or assume that they are in equilibrium with calcium (the rapid buffering approximation). In this article we address the issue of whether this approximation provides a good description of wave propagation. We first compare the timescales present in the problem, and determine the situations in which the equilibrium hypothesis fails. We then present a series of numerical studies based on the simple fire-diffuse-fire model of wave propagation. We find that the differences between the full and reduced descriptions may lead to errors that are above experimental resolution even for relatively fast buffers in the case of saltatory waves. Conversely, in the case of continuous waves, the approximation may give accurate results even for relatively slow buffers.

Receptors, sparks and waves in a fire-diffuse-fire framework for calcium release

Calcium ions are an important second messenger in living cells. Indeed calcium signals in the form of waves have been the subject of much recent experimental interest. It is now well established that these waves are composed of elementary stochastic release events (calcium puffs or sparks) from spatially localised calcium stores. The aim of this paper is to analyse how the stochastic nature of individual receptors within these stores combines to create stochastic behaviour on long time-scales that may ultimately lead to waves of activity in a spatially extended cell model. Techniques from asymptotic analysis and stochastic phase-plane analysis are used to show that a large cluster of receptor channels leads to a release probability with a sigmoidal dependence on calcium density. This release probability is incorporated into a computationally inexpensive model of calcium release based upon a stochastic generalisation of the fire-diffuse-fire (FDF) threshold model. Numerical simulations of the model in one and two dimensions (with stores arranged on both regular and disordered lattices) illustrate that stochastic calcium release leads to the spontaneous production of calcium sparks that may merge to form saltatory waves. Illustrations of spreading circular waves, spirals and more irregular waves are presented. Furthermore, receptor noise is shown to generate a form of array enhanced coherence resonance whereby all calcium stores release periodically and simultaneously.

Imaging calcium entering the cytosol through a single opening of plasma membrane ion channels: SCCaFTs—fundamental calcium events

Recently, it has become possible to record the localized fluorescence transient associated with the opening of a single plasma membrane Ca(2+) permeable ion channel using Ca(2+) indicators like fluo-3. These Single Channel Ca(2+) Fluorescence Transients (SCCaFTs) share some of the characteristics of such elementary events as Ca(2+) sparks and Ca(2+) puffs caused by Ca(2+) release from intracellular stores (due to the opening of ryanodine receptors and IP(3) receptors, respectively). In contrast to intracellular Ca(2+) release events, SCCaFTs can be observed while simultaneously recording the unitary channel currents using patch-clamp techniques to verify the channel openings. Imaging SCCaFTs provides a way to examine localized Ca(2+) handling in the vicinity of a channel with a known Ca(2+) influx, to obtain the Ca(2+) current passing through plasma membrane cation channels in near physiological solutions, to localize Ca(2+) permeable ion channels on the plasma membrane, and to estimate the Ca(2+) currents underlying those elementary events where the Ca(2+) currents cannot be recorded. Here we review studies of these fluorescence transients associated with caffeine-activated channels, L-type Ca(2+) channels, and stretch-activated channels. For the L-type Ca(2+) channel, SCCaFTs have been termed sparklets. In addition, we discuss how SCCaFTs have been used to estimate Ca(2+) currents using the rate of rise of the fluorescence transient as well as the signal mass associated with the total fluorescence increase.